Search for Intermittent X-ray Pulsations from Neutron Stars in Low Mass X-ray Binaries
PPublications of the Astronomical Society of Australia (PASA)doi: 10.1017/pas.2021.xxx.
Search for Intermittent X-ray Pulsations from NeutronStars in Low Mass X-ray Binaries
Yunus Emre Bahar , Manoneeta Chakraborty and , Ersin Göğüş Sabancı University, Faculty of Engineering and Natural Sciences, Orhanlı Tuzla 34956 Istanbul Turkey DAASE, Indian Institute of Technology Indore, Khandwa Road, Simrol Indore 453552, India
Abstract
We present the results of our extensive binary orbital motion corrected pulsation search for 13 low massX-ray binaries (LMXBs). These selected sources exhibit burst oscillations in X-rays with frequenciesranging from 45 to 1122 Hz, and have a binary orbital period varying from 2.1 to 18.9 hours. We firstdetermined episodes that contain weak pulsations around the burst oscillation frequency by searchingall archival Rossi X-ray Timing Explorer (RXTE) data of these sources. Then, we applied Dopplercorrections to these pulsation episodes to discard the smearing effect of the binary orbital motion andsearched for recovered pulsations at the second stage. Here we report 75 pulsation episodes that containweak but coherent pulsations around the burst oscillation frequency. Furthermore, we report eight newepisodes that show relatively strong pulsations in the binary orbital motion corrected data.
Keywords: methods: data analysis – stars: neutron – X-rays: binaries – X-rays: stars
Neutron stars in low mass X-ray binaries (LMXBs) areamong the brightest sources in the X-ray sky. Theiremission is predominantly powered by the accretion ofmatter from the Roche lobe filled late type companionstar; namely, the conversion of the gravitational poten-tial energy of the infalling material into radiation nearor on the surface of the compact object. As a result,such neutron stars either emit continuously (persistentsources) or only when the accretion mechanism is rein-stated (transient sources). There are plethora of charac-teristic observational imprints in their X-ray emission,such as twin quasi-periodic oscillations (QPOs) in thekHz regime (van der Klis et al., 1997), thermonuclear X-ray bursts with oscillations (Watts, 2012). However, themajority of nearly 200 known neutron stars in LMXBsdo not emit coherent X-ray pulsations.Accreting millisecond X-ray pulsars (AMXPs) hasemerged as a subclass of neutron star in LMXBs inthe last two decades (Patruno & Watts, 2012). Thesetransient systems exhibit coherent pulsations with pe-riods shorter than ∼
10 ms. The remarkable capabilityof AMXPs to turn the accretion energy into pulsationsraises a question regarding the reason behind the lackof X-ray pulsations from the majority of the LMXBs. ∗ [email protected] There might be no emerging pulsations from major-ity of LMXBs possibly because of insufficient magneticfield strengths to channel the accreting matter to themagnetic pole. Alternatively, the beamed signal couldalready be present but weak; it might be further weak-ened to non-detection while emerging pulsed radiationundergoes various dynamical or physical processes. De-tection of intermittent episodes of coherent pulsationsin the persistent emission phase from couple of systems(Aql X–1, Casella et al. (2008); SAX J1748.9–2021, Al-tamirano et al. (2008)) support the case that all neutronstars in LMXBs are likely to radiate X-ray pulse. Theseobservations provided a unique opportunity to betterunderstand the reason of appearance and then disap-pearance of the pulsed emission.There are various neutron star atmosphere and sur-roundings effects that can reduce the pulse amplitude,and in turn, lead to the lack of pulsations. The mostnotable scenarios for this situation include light bendingeffect resulting from the extreme gravity of the compactobject (Wood et al., 1988; Özel, 2009), scattering charac-teristics of the environment surrounding the neutron star(Brainerd & Lamb, 1987; Titarchuk et al., 2002), andthe magnetohydrodynamic instabilities in the accretionflow (Kulkarni & Romanova, 2008). Another possiblecause is the binary orbital motion, which could smearthe already weak signal to non-detection. Such a dy-1 a r X i v : . [ a s t r o - ph . H E ] F e b Bahar et al. namical effect would introduce significant implicationson the pulsed signal especially in tight binary systems.In such systems, it could, in principle, be possible torecover a pulsed signal in the X-ray data if the binaryorbital effects are accounted for.There have been several extensive studies to correctsmearing of pulsations due to dynamical effects frombinary neutron stars. One approach, the accelerationsearch provides a partial correction by splitting thedata into short segments and assuming that the orbitalacceleration of the neutron star to be approximatelyconstant during the segments of the binary orbit whichcorresponds to the exposure time of the obsevation (e.g.Middleditch & Kristian, 1984; Anderson et al., 1990;Wood et al., 1991). Later, Ransom et al. (2001, 2002)elaborated this technique to obtain template responsesin the frequency - frequency derivative ( f - ˙ f ) plane. Theycorrelate the Fourier amplitude and phase responses ofthe real time data with template responses that aregenerated with trial acceleration values. Recently, it wasextended by assuming jerk ( ¨ f ) to be constant, insteadof the orbital acceleration (Andersen & Ransom, 2018).By doing that they added one more dimension to theirparameter space and conducted their search in f - ˙ f -¨ f volume which they called jerk search (Andersen &Ransom, 2018). These methods are widely employed tosearch for periodic signal in timing data collected in theradio band.Another approach to detect smeared pulsations iscalled semi-coherent search. It was first proposed asa technique to detect weak gravitational wave signals(Messenger, 2011), and then applied to search for weakX-ray signals from neutron stars in LMXBs (Messenger& Patruno, 2015; Patruno et al., 2018). The focus ofthis method is to detect weak but continuous pulsations.They attempted to achieve this goal by applying a two-step procedure on the X-ray data. In the first stage,they divide data to segments and process each segmentwith a bank of templates coherently. These templatesare produced such that they account for the Dopplermodulation in the phase of the signal by a Taylor expan-sion in frequency. In the second stage they incoherentlycombine the coherent signal power results obtained foreach segment. They applied this technique to 12 LMXBsand no evidence was found for a previously non-detectedweak pulsation.Physical mechanism behind pulse smearing is the rel-ativistic Doppler effects caused by the rotational motionof the neutron star around the common center of mass ofthe binary system. Effectively, Doppler effects modulatethe signal by causing delays on the photon arrival timesdepending on the relative position of the neutron staron its orbit. This delay was formulated by Blandford& Teukolsky (1976) for observing and testing variousrelativistic effects by making use of the information thatpulsars are reliable and precise clocks. In this study, we use this formulation to revert the effect of the bi-nary orbital motion to possibly strengthen the pulsedsignal. Smearing can redistribute the signal power toother frequencies around the actual frequency such thatthe power of the smeared signal lies near or below thedetection threshold. We, therefore, applied a systematicinvestigation by first correcting the arrival times of pho-tons including pulsed signals that are just below thedetection level, and then searched for periodic signal inthe corrected data. Note that earlier strategies to searchfor weak pulsations relied on sophisticated templatesto model the binary effects on the coherent pulsationsignal. In our method, we first account for the smear-ing effect by transforming the photon arrival times toan inertial frame at the common center of mass of thebinary system and then use a simple sinusoidal modelto measure the strength and the frequency of the pulsedsignal.Here we present the results of our extensive search fortransient episodes of pulsed X-ray emission in the entireRossi X-ray Timing Explorer (RXTE) data of 13 binaryneutron stars systems, as well as our investigations toconstrain the orbital characteristics of these systems. We performed the search for weak pulsations in twosteps. In the first tier, we conducted pulse search on thebarycentered data and determined the candidates. Inthe second step, we applied arrival time corrections tothese candidates to account for the effects of the binarymotion and re-searched for pulsations in the correcteddata. st Tier Search andResults
For the first tier pulsation search, we selected 13 neutronstar low mass X-ray binary and used all available eventmode archival RXTE data. Note that none of thesesources show X-ray pulsations above the noise level dur-ing their persistent emission phase (except Aql X–1).However, ten of them show prominent quasi-periodicoscillations just before, during or just after they ignite athermonuclear X-ray burst. Remaining three also havereported periodicities in their burst observations. Nev-ertheless, these sources (XTE 1739–285, A 1744–361,GS 1826–238) show either only one burst or the burstoscillations are tentative. We assume that thermonu-clear burst oscillations correspond to an X-ray emittinghotspot and the spin frequency of the underlying sourceis around the frequency of these oscillations (see Watts(2012)). Binary orbital periods of six of these sourcesare known either from periodicities or eclipses observedin the X-ray data. We present the list of the sourcesinvestigated and their burst oscillation frequencies in
Table 1
Fundamental characteristics and RXTE observational details of the systems investigated
Source Burst Oscillation Orbital Average Count Rate Total Time ReferencesFrequency f s (Hz) Period P b (Hr) ( counts s − P CU − ) b Searched t tot (ks)EXO 0748–676 45/552 a a There are two different burst oscillation frequencies reported for EXO 0748–676. b Average count rates are calculated in the energy range of ∼ References–
1. Villarreal & Strohmayer (2004); 2. Galloway et al. (2010); 3. Altamirano et al. (2010); 4. Markwardt et al. (1999); 5.Strohmayer et al. (1996); 6. Smith et al. (1997); 7. Muno et al. (2000); 8. Bhattacharyya et al. (2006); 9. Chevalier & Ilovaisky (1991);10. Zhang et al. (1998); 11. Welsh et al. (2000); 12. Casella et al. (2008); 13. Wijnands et al. (2001); 14. Strohmayer et al. (1998); 15.Strohmayer & Markwardt (2002); 16. Kaaret et al. (2002); 17. Galloway et al. (2008); 18. Thompson et al. (2005); 19. Hartman et al.(2003); 20. Wachter et al. (2002); 21. Kaaret et al. (2007);
Table 1.Before applying the first tier search, we generatedthe light curve of each RXTE pointing in the 2–60 keVenergy band with 0.125 s time resolution to search forthermonuclear X-ray bursts. We then created good timeintervals for each source by excluding the times of iden-tified X-ray bursts. In particular, we excluded the datastarting 20 seconds before the burst peak till 200 secondsafter. This conservative selection excludes any possiblecontribution from even the relatively longer durationbursts. Note that the source 4U 1728–34 has a type-IIX-ray burster (the Rapid Burster) in its RXTE PCAfield of view. For this system, we ignored all observationswith type-II bursts present and excluded them from ourlist of good time intervals. We list the total investigatedobserving time for each source after the exclusion of theburst intervals in Table 1. Finally, we transferred thephoton arrival times to the Solar System barycenter toget rid of the relativistic effects of the moving frame ofthe detector.In the first tier search, we fixed channel ranges fromone observation to the other rather than fixing energyranges because energy-channel relation of RXTE haschanged during its lifetime. This did not create anyproblem since we have not compared any observationto the other directly. We applied statistical analysistechniques for comparing any result to the other.To make our search sensitive for the pulsations thatare made up of only hard or low energy X-ray photons, we carried out the first step of our pulsation search inthree energy bands; ∼ ∼ ∼ f s ±
10 Hz where f s isthe reported burst oscillation frequency. Note the factthat intermittent weak pulsations are non-stationaryby definition. This makes it harder to decide how todeal with the number of trials while converting the sig-nal powers to its corresponding statistical significancevalues. We decided to calculate statistical significancevalues by considering each power spectrum on its ownand avoid confusion by providing the power levels be-sides the significance levels. Therefore, first the singletrial probability of obtaining the highest Leahy power isfound and then joint probability of having the spectrumis calculated with the number of trials ( N trials ) equal to Bahar et al. the number of frequency bins searched i.e., the number offrequency bins between f s ±
10 Hz. At last, significancelevel of this joint probability is calculated from a normaldistribution in the light of the central limit theorem.Here we have calculated the Gaussian significance of thejoint probability by considering a two-tailed test giventhe p-value. It is to be noted that the significance valuesdo not change by an appreciable amount if one-sidedtest (considering one tail of the Gaussian) is applied. Wethen slided the 256 s interval by 16 seconds, repeatedthe same procedure to obtain the significance for thattime interval, and continued until the end of the observa-tion. This procedure would facilitate the detection andstrengthening of any signal which is present of a shorttime duration.After calculating the statistical significance of thestrongest pulse for each window, we selected candidatesby applying the following continuity, coherence and min-imum significance criterion. We require a pulsation can-didate for further detailed analysis to have at least 2.5 σ statistical significance for four consecutive time segmentsand having the maximum Leahy power between f s ± ∼ Z test (Buccheri et al., 1983)which is computationally more expensive but it doesnot require the data to be binned. The Z power isformulated as Z n = 2 N n X m =1 [ { N X j =1 cos( mφ j ) } + { N X j =1 sin( mφ j ) } ] (1)where n is the number of harmonics, N is the totalnumber of photons, and φ j is the phase of the j th photon. Z powers are distributed with a χ distribution with 2 n degrees of freedom where n corresponds to the desirednumber of harmonics. In our case, we have chosen thenumber of harmonics to be 1 since strong harmonics arenot reported for the sources of interest. The Z powersare calculated with a 1/512 Hz frequency resolutionbetween f s ± Until this point, we searched for coherent pulsationsin the data that only the barycentric correction wasapplied. However, binary orbital motion of the neutronstar could smear out an already weak signal and makeit undetectable. In our study, we used the appropriaterelativistic orbit model (Blandford & Teukolsky, 1976)for the Doppler correction to be able to recover thesmeared signal based on plausible orbital parameters.The time delay, t d due to orbital motion is formulatedas t d = { α (cos E − e ) + ( β + γ ) sin E }× (cid:26) − πP b β cos E − α sin E − e cos E (cid:27) (2)where α = x sin w and β = (cid:0) − e (cid:1) / x cos w areexpressed in terms of the projected semi-major axis, x = a sin i , P b is the binary period, E is the eccentricanomaly, e is the eccentricity, w is the longitude of peri-astron and γ is the term for the gravitational redshiftand time dilation. The eccentric anomaly E is definedas E − e sin E = 2 πtP b (3)from the Kepler’s equation (Taylor & Weisberg, 1989).In our search we assumed the orbit of the neutron starto be circular which is a plausible approximation forLMXBs ( e = 0). This assumption reduced the numberof free parameters to three that are the binary orbitalperiod ( P b ), projected semi-major axis ( x ) and the epochof mean longitude equal to zero ( T ). Because of thelack of information and uncertainties about the epoch ofmean longitude equal to zero, we decided to apply a π/ ψ ) of the circular orbitthat corresponds to 8 trial phases in total. This way, weaimed to test roughly all possible configurations thatcan effect the signal. For the six sources whose binaryorbital periods were already reported (see Table 1), welimited the search interval of binary period to within 1hr around their reported value, with a 0.1 hr sampling Figure 1.
Example of a candidate pulsation episode from 4U 1636–536 that lasts for five consecutive time windows. The pulsationcandidate and its properties are indicated in boldface in Table 3. (top panel)
The light curve of the part of the observation that contains336 s long candidate pulsation episode. The vertical dashed lines that have the same line style correspond to the starting and endingtime of 256 s windows from which power spectra are calculated. (bottom plots) Z power density spectra of the five sequential 256 sintervals indicated with vertical lines above. The signal at 579.66 Hz is clearly evident in all plots. in those 2 hr intervals. For the rest of the sources whosebinary period is unknown, we chose the range of thetrial range of orbital periods to be 2–30.5 hr and applied1.5 hr sampling to this time interval. This orbital periodinterval is expected to correspond to a great majorityof LMXB orbital periods (van Haaften et al., 2015).Similar to the uncertainties about the epoch of meanlongitude equal to zero ( T ) of the sources, projectedsemi-major axis ( x ) values of LMXB sources were alsoeither unknown or highly uncertain. For this reason, weselect a broad range of trial values from 0.01 to 1.91light-s with 0.1 light-s sampling. Therefore, for each 256s pulsation candidate time segment, the correction isapplied for 8 × ×
20 sets of parameters which span T , P b and a sin i parameters, respectively. Sampling sizes ofthe correction parameters were limited mainly due to thecomputational costs. We tried to cover a wide range ofparameters with the smallest grid size possible given thepresent computational capabilities. We would like to alsonote that the reported binary periods of our six sourcesare much greater than 256 s. In practice, one couldreduce the parameter space further based on this fact(see Ransom et al. (2001, 2002)). However, we decided topursue with the Blandford & Teukolsky (1976) correctionand applied it in all three dimensions for the sake ofcompleteness and for creating a generalized approachapplicable to different sources.We then searched for pulsations in the binary orbitalmotion corrected data by employing the Z methodbetween f s ± f max ) from the firstorder calculations∆ f max = f p (cid:12)(cid:12)(cid:12)(cid:12) P b P b − πa sin i − (cid:12)(cid:12)(cid:12)(cid:12) (4)and then located recovered pulsations by applyingthe following set of criterion: We require the recoveredpulsations to have at least 3.5, 4.5 and 3.5 σ statisticalsignificance for three consecutive time segments andwe require significance values for these three segmentsto be higher than before (that is, before the binarymotion correction). We choose these significance levelssince we wanted to put a significance criterion at least1 σ higher than the previous (2.5 σ ) for the detectionof the recovered pulses. We require the improvementin the significance levels for three time segments to beachieved concurrently after corrected with the sameparameter set. We also require the pulsations to be atthe same frequency for these three time segments andthe frequency of the recovered pulsation to be at most∆ f max away from the frequency of the pulsation beforecorrection.After applying this set of criterion we identified re-covered pulsations for five sources; EXO 0748–676, 4U1608–52, 4U 1636–536, Aql X–1, 4U 1728–34 out of 10that showed pulsation candidates. We obtained degener-ate pulsations for almost all time segments that showrecovered pulsations. These pulsations were degeneratesuch that, for a single time segment there were manyrecovered pulsations that were obtained with different P b , a sin i , and ψ parameter sets. Moreover, pulsationstrengths of recovered pulsations for a single time seg-ment were at a similar level. The presence of degenerate Bahar et al. recovered pulsations was expected because of the degen-erate nature of Doppler effects. For example, to obtainsimilar Doppler effects for a trial orbital phase thereshould be a relation between P b and a sin i such that if P b is short, a sin i should also be shorter to compensateeach other.Binary orbital period ( P b ) of four of the five sourceswere already known (except 4U 1728–34). This helped usto eliminate the degenerate cases of recovered pulsations.We discarded the recovered pulsations that are obtainedwith a P b that is different than the reported P b . Further-more, for each time segment we selected the parameterset that gives the the highest signal power among theones that have the appropriate P b . Since we did not knowthe binary period of 4U 1728–34, we adopted a slightlydifferent approach. Since sampling for the P b parameterof 4U 1728–34 is 15 times larger than the ones that thebinary periods are known, we decided to decrease thesignificance criterion of the detection of the recoveredpulsation to 3.5, 4.0 and 3.5 from 3.5, 4.5 and 3.5. Bydoing so, we aimed to report more recovered pulsationsand corresponding P b , a sin i couples for such a highlyunknown situation. We list the results of the recoveredpulsations and the corresponding correction parametersin Table 2. Note that we also report in Table 2 the binarymotion corrected results for the previously detected 150s intermittent pulsation episode from Aql X–1 (Casellaet al., 2008). Each line in this table corresponds to a 256second time window that meets our detection criteriaand it can be seen that some of these time windows areadjacent to each other. We count the adjacent windowsas one pulse episode which makes a total of eight newpulsation episodes reported in the table excluding thedetection of Casella et al. (2008).There were two different spin frequencies in literaturethat thought to be related with the spin frequency ofEXO 0748–676 that are 45 and 552 Hz. We were able toobtain pulsation candidates at both of these frequenciesin our first tier search. However, after applying and cor-recting the photon arrival times, we obtained recoveredpulsations only around 45 Hz even though smearingeffect of the Doppler modulation is increasing at higherfrequencies. We have performed one of the most comprehensivesearch for intermittent pulsation episodes in non-pulsingLMXBs. In particular, we have accounted for the binaryorbital motion systematically in our extensive inves-tigations. Recently, Messenger & Patruno (2015) andPatruno et al. (2018) also accounted for the Dopplershift in searching pulsations from LMXBs with theirsemi-coherent search. Their work differ from ours ata fundamental level: They aimed to detect continuousbut weak pulsations, contrary to our search for inter- mittent pulsation episodes. Furthermore, eight out of 12of their LMXB sample did not show burst oscillations.This made their parameter space significantly wider forthese LMXBs contrary to more confined spin frequencyparameter in our work thanks to the previously reportedburst oscillations for the LMXBs. Note that we havenine different LMXBs in addition to four common withtheir work, namely; Aql X–1, 4U 1636–536, 4U 1608–52and XTE 1739–285.Detection of a single ∼
150 s long pulsation episode(Casella et al., 2008) in the entire archival RXTE dataof Aql X–1’s persistent emission phase clearly show thatthe intermittent pulsations are very rare (0.009% of thetotal 1645 ks observed time). Note that the pulsationepisodes in other sources are also rare with respect tothe total observation time: 0.023% for EXO 0748–676,0.012% for 4U 1608–52, 0.016% for 4U 1636–536 and0.062% for 4U 1728–34. We should note here that occur-rence rate for 4U 1728–34 is expected to be higher sincewe lowered significance criterion for this source. (SeeSection 2.2). Besides these recovered pulsations, we alsofound pulsation candidate episodes that contain weakpulsations around the burst oscillation frequencies forall 13 LMXBs in our sample. These candidate episodesare also short and rare compared to the total searchedtime of each source: 0.24% for EXO 0748–676, 0.08% for4U 1608–52, 0.13% for 4U 1636–536, 1.84% for MXB1658–298, 0.07% for 4U 1702–429, 0.21% for 4U 1728–34,0.52% for XTE 1739–285, 0.15% for SAX J1750.8–2900,0.12% for GS 1826–238, and 0.19% for Aql X–1Strohmayer et al. (2018) employed the same binary or-bital motion correction to account for Doppler smearingin an accreting millisecond X-ray pulsar system, IGRJ1762–6143 with an ultra-compact orbit (binary orbitalperiod is ∼
38 min). They found that the orbital delaysweaken the pulsation such that after the correction to itsNICER data, Z power of the pulsation increase up to ∼
196 which is almost 4 times the previous value ( ∼ P b ) sources consideringthe high uncertainties in the inclination angles.We were able to determine orbital inclination of four Table 2
Results of the binary motion corrected search
Source Time (UTC) a P b a sin i f Z Z sig Z (Hr) (lt-s) (Hz) Power ( σ )EXO 0748–676 1998 Mar 14 01:02:20.9 3.82 1.81 44.48 41.30 4.732009 Jul 28 08:30:34.0 3.82 1.71 46.43 43.72 4.974U 1608–52 2007 Nov 1 06:39:58.1 12.89 1.91 619.28 39.42 4.544U 1636–536 2002 Jan 8 18:13:46.4 3.80 0.61 580.57 40.33 4.632006 Apr 23 11:21:54.8 3.80 0.61 579.82 41.17 4.722006 Apr 23 11:22:26.8 3.80 1.71 580.12 40.05 4.61Aql X–1 b c a Time (UTC) is the starting time of the 256 s time window. b Lines under Aql X–1 are orbital motion corrected results of the previously discovered 150 s pulsation episode by Casella et al. (2008) c Detection criterion of recovered pulsations for 4U 1728–34 is different than other sources which is 3.5, 4.0 and 3.5 rather than 3.5, 4.5and 3.5 for three consecutive time segments. See Section 2.2 for a more detailed discussion. systems, based upon our criterion that the search inthe Doppler corrected data would yield the strongestsignal. We suggest the projected semi-major axis ( a sin i )value of about (5.1–5.4) × m for EXO 0748–676, and5 . × m for 4U 1608–52. For typical orbital separa-tions ( a ) that can be calculated from the known binaryperiods, the orbital inclination of these two systemsturned out as 29.0–30.9 and 13.9 degrees, respectively.Our search for projected semi-major axis of 4U 1636–536and Aql X–1 concentrate around two values: 1 . × or5 . × m for the former, and 3 . × or (5.1–5.7) × for the latter. These correspond to 9.9 or 29.1 degrees ofinclination for 4U 1636–536 and 6.2 or 9.6–10.7 degreesfor Aql X–1. We would like to note that, donor massand neutron star mass are assumed to be 0.5 and 1.4 M (cid:12) respectively for calculating the orbital separations.Highly degenerate recovered pulsations and their scat-tered orbital parameters in the P b – a sin i plane madeit impossible to determine orbital parameter estimatesfor 4U 1728–34. Two recovered episodes of pulses forEXO 0748–676 were found at the frequencies of 44.5 and46.4 Hz. We found pulsation candidate episodes around552 Hz, which is the other suggested frequency, and alsothere are other studies supporting that (Balman, 2009;Jain & Paul, 2011). However, we did not detect any re-covered pulsations after the Doppler correction around the higher frequency. In the light of these results, weargue that the 45 Hz may be the actual spin frequencyof EXO 0748–676 rather than 552 Hz.We have also investigated whether X-ray intensity(that is a measure of mass accretion rate) is differentduring those pulsation episodes. We compare the averagecount rate for each source (listed in Table 1) to thesource rates during the episodes of coherent pulsations(listed in Table 2). We find no systematic trend in X-ray intensities, neither higher nor lower than their longterm averaged values. We, therefore, suggest that theappearance of pulsations are not linked to any suddenchange in the accretion rate.The lack of pulsations in these bright LMXB sourcesmay not be solely related to the Doppler effects. Thereare already numerous suggestions attempting to explainthe reason of intermittent pulsations. Sporadic behaviourand uncommon nature of such periodicities force theexplanations to be somehow related with a rare incidentor asymmetry that might be taking place close to theneutron star surface. These explanations can be roughlydivided into two categories: one group of explanationsassume that the pulsation is temporary while other groupassume that the pulsation is always present however soweak that we cannot detect it.One possible explanation for the lack of pulsations Bahar et al. that belongs to the first group is the scattering of thebeamed emission by the optically thick media. However,this approach was challenged by Göˇgüs , et al. (2007)where they argued through spectral investigations thatthe optical depth τ of the surrounding corona is not thickenough to smear out the pulsations. In order for thisexplanation to work, temperatures of scattering electronsshould be very low ( (cid:46)
10 keV) so that the optical depthwould be large enough to screen. The pulsations wouldthen become visible only during a spectral variability,in presence of a local hole in the screening mediumor in presence of other unique asymmetric geometries(Casella et al., 2008). In such a scenario, one would alsoexpect a dependence of the presence of the pulsationon the accretion rate as in such systems the coronalproperties are strong function of the accretion rate. Sucha correlation was found to absent in our analysis.The second group of explanations is generally relatedto the magnetic channeling. Neutron stars in LMXBs areweakly magnetized. Therefore, they are typically unableto stop and focus the incoming matter. The appearanceof pulsations could either be due to a sudden changein the amount of channeled matter or the strength oftheir magnetic field could suddenly increase (at leastlocally) and become capable of channeling matter. Thesecond scenario might occur if there is a sudden decreasein the Ohmic diffusion time which could happen dueto a starquake, local disruption of screening currentsor magnetic reconnections (Casella et al., 2008). It isessential to study multipolar magnetic fields in suchneutron stars to find an evidence for strengthening themagnetic fields. Recent serious efforts to understandmagnetic field structure of neutron stars by ray-tracingtechnique (Bilous et al., 2019) may provide new insightson this front.Another approach within the second group explana-tions is nuclear burning. We expect nuclear poweredoscillations to last typically a few seconds. However,Strohmayer & Markwardt (2002) reported a long-lastingpulsation during a superburst of 4U 1636–536. This in-dicates that coherent and longer lasting oscillations mayalso be related with nuclear burning. This explanationcannot be related with our results since we carefullyidentified the bursts and eliminated their times fromour searched sample. There could, in principle, be nu-clear burning events which might not be seen radiatively(as thermonuclear bursts) but the stored energy couldinstead give rise to intermittent coherent oscillations.
We are grateful to the anonymous reviewer for conservativecomments. We acknowledge support from the Scientific andTechnological Research Council of Turkey (TÜBİTAK, grantno: 115R034).
Table 3
Results of the first tier pulsation search
Source Time (UTC) a t dur Leahy Z f L sig L Count Rate(s) b Power c Power c (Hz) c ( σ ) c ( counts s − P CU − ) d EXO 0748–676 1998 Mar 14 01:02:04.9 320 35.9 35.7 44.51 3.94 36.81998 Jun 28 13:37:49.0 352 33.9 32.9 45.77 3.70 35.32000 Mar 28 15:43:36.9 320 36.8 36.2 46.09 4.04 39.92002 Sep 1 12:38:55.0 320 29.0 29.1 44.18 3.01 22.92003 Feb 15 07:00:09.0 304 35.1 34.9 45.04 3.84 31.02003 Aug 18 19:46:36.0 304 31.9 31.1 44.75 3.43 40.12004 Apr 26 15:06:20.0 320 28.7 29.6 46.55 2.96 51.52004 Apr 26 15:24:12.0 320 32.4 32.0 45.55 3.50 55.12004 Nov 25 15:58:35.9 304 29.5 29.4 43.55 3.09 45.92007 Feb 7 08:26:53.0 304 35.3 35.9 45.46 3.87 16.82007 Aug 23 20:57:00.1 304 28.8 29.5 46.29 2.98 39.22009 Jul 28 08:30:02.0 320 39.3 40.3 46.41 4.33 20.41997 Jan 19 12:28:17.0 304 27.2 14.6 552.40 2.73 31.02004 Sep 25 15:02:52.0 304 38.5 40.1 550.20 4.24 15.02006 Sep 16 16:49:15.0 352 34.2 28.0 553.27 3.73 33.92008 Feb 3 09:51:06.9 336 28.6 23.6 551.63 2.95 14.92008 Feb 6 19:22:03.0 304 35.0 33.3 553.14 3.83 42.24U 1608–52 2002 Sep 1 09:25:30.0 304 32.0 28.6 620.13 3.45 746.32002 Sep 28 18:26:26.0 320 31.7 29.7 620.53 3.40 46.22003 Oct 4 17:11:39.0 304 30.6 20.6 620.80 3.25 70.82007 Nov 1 06:39:10.1 304 30.2 30.0 619.28 3.19 1298.82008 Nov 3 01:33:26.0 320 32.7 20.6 621.64 3.54 119.32011 Dec 17 22:43:10.0 320 31.3 21.6 621.14 3.35 66.04U 1636–536 2001 Sep 30 14:10:38.0 336 35.3 31.1 580.08 3.86 242.22001 Oct 3 17:41:54.0 304 29.2 26.6 582.29 3.04 246.82002 Jan 8 14:31:39.2 320 30.4 22.4 579.86 3.21 201.72002 Jan 8 18:13:14.4 336 35.8 39.5 580.41 3.93 186.12002 Jan 14 08:40:11.7 304 28.8 30.2 582.35 2.98 158.92002 Feb 28 18:30:51.8 320 27.7 23.2 582.29 2.81 534.12002 Mar 19 17:09:15.9 304 29.3 20.1 579.61 3.05 387.52005 Aug 29 18:49:32.2 320 35.3 27.8 580.05 3.87 112.32005 Aug 30 11:57:00.2 320 32.0 22.5 580.11 3.44 119.1 e
336 30.2 40.3 579.66 3.20 188.3
Bahar et al. f
336 76.3 94.7 550.27 7.39 894.32002 Mar 27 15:35:45.9 336 33.0 27.6 549.50 3.57 29.92005 Apr 6 07:31:47.8 304 28.6 29.8 551.62 2.94 138.82005 May 12 05:50:18.9 320 27.8 22.4 551.93 2.82 34.32005 May 15 20:08:27.9 304 31.7 28.5 551.44 3.41 22.62007 May 29 16:26:57.9 320 32.4 28.2 551.53 3.50 113.52007 May 31 00:11:54.9 336 36.5 24.6 550.70 4.01 132.32007 Jul 2 12:28:41.0 304 33.5 25.3 551.00 3.64 17.7 a Time (UTC) is the starting time of the candidate pulsation episode. b t dur is measured from the starting time of the first time segment to the ending time of the last time segment that fits our detectioncriterion of 2.5 σ statistical significance in four consecutive time segments. c Leahy power, Z power, f L and sig L are obtained from the time segment where the strongest pulsation is observed within thecorresponding pulsation episode. d Count rates during the candidate pulsation episodes in the energy range of ∼ e This is the pulsation that is shown in Fig 1. f This is already reported as an intermittent pulsation by Casella et al. (2008). REFERENCES
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